Upon baking animation to controls, it might produce such issues that cause gimbal locking, which you probably are experiencing. You'd select all the rotation curves for that object and apply GraphEd > Curves > EulerFilter.
And, if it is HIK rig, then, not sure, but it might be with Quaternion rotations which would make jumps intentionally to keep animation in some range, e.g. -180°..+180°.
If you can afford it, consider changing the rig control's rotation order to the one that causes less gimbal locking, and it is possible, without loosing the animation, with a script, the only thing is it will generate keys every keyframe, which you can clean with some other filters in the Curve menu.
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Maya2019.1 @ Windows10 & GeForce GTX1080Ti
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